The Lagrange multiplier method is the method of finding a conditional extremum of the function:
fx, xϵRn according to a number of m constraints where i is from 1 to m.
The algorithm is the following:
- Form the Lagrange function as a linear combination of the function f and functions φi, taken with the coefficients, called Lagrange multipliers – λi: where - Construct the system of m+n equations, equating to zero the partial derivatives of the Lagrangian by and - If the resulting system has a solution with respect to parameters and , then may be conditional extremum, i.e. the solution of the original problem. Note that this condition is necessary but not sufficient character.
Application
Lagrange multipliers method is ...
